Chaos of a Markov Operator and the Fourth Moment Condition
نویسنده
چکیده
– We analyze from the viewpoint of an abstract Markov operator recent results by D. Nualart and G .Peccati , and I. Nourdin and G. Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian distribution. Convergence to gamma distributions may be examined similarly.
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تاریخ انتشار 2011